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A145525 Numbers X such that there exists Y in N : X^2=273*Y^2+91. 1
182, 264446, 384504302, 559068990662, 812885927918246, 1181935580124139022, 1718533520614570219742, 2498746557038004975365846, 3633175775399738619611720342, 5282635078684662914910466011422, 7680947771231724478541197968887246 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (1454,-1).

FORMULA

a(n+2) = 1454*a(n+1)-a(n).

a(n) = 91*{[727-44*sqrt(273)]^n+[727+44*sqrt(273)]^n}-(11/2)*sqrt(273)*{[727-44*sqrt(273)]^n -[727+44*sqrt(273)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: -182*x*(x-1) / (x^2-1454*x+1). - Colin Barker, Oct 21 2014

EXAMPLE

a(1)=182 because the first relation is 182^2=273*11^2+91.

MATHEMATICA

LinearRecurrence[{1454, -1}, {182, 264446}, 20] (* Harvey P. Dale, Nov 03 2012 *)

CoefficientList[Series[182 (1 - x)/(x^2 - 1454 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

PROG

(PARI) Vec(-182*x*(x-1)/(x^2-1454*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014

(MAGMA) I:=[182, 264446]; [n le 2 select I[n] else 1454*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 21 2014

CROSSREFS

Sequence in context: A225712 A015306 A190830 * A028676 A228535 A248628

Adjacent sequences:  A145522 A145523 A145524 * A145526 A145527 A145528

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 12 2008

EXTENSIONS

Editing from Colin Barker, Oct 21 2014

STATUS

approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)